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The expression $-f(x-5)$ represents a reflection across the x-axis combined with a horizontal shift 5 units right, because the negative sign is outside the function. The expression $f(-x-5)$ represents a reflection across the y-axis combined with a horizontal shift 5 units right, because the negative sign is only on the input variable $x$ inside the function.

Conditions: The base function is $y=f(x)$.; Both expressions include a horizontal shift 5 units right.

The expression $-f(x-5)$ represents a reflection across the x-axis combined with a horizontal shift 5 units right, because the negative sign is outside the function. The expression $f(-x-5)$ represents a reflection across the y-axis combined with a horizontal shift 5 units right, because the negative sign is only on the input variable $x$ inside the function.

Conditions: The base function is $y=f(x)$.; Both expressions include a horizontal shift 5 units right.